Friction Numbers and Viscous Dissipation Heating for Laminar Flows of Water in Microtubes

Abstract

The friction numbers for laminar flows of water in microtubes, determined from the temperature rise due to the viscous dissipation heating assuming a velocity slip, show a strong dependence on the diameter and aspect ratio. The calculated values compare well with those determined from experimental data for water flows in glass and diffused silica microtubes (16–101μm in diameter D and aspect ratios L∕D=499–1479). With a slip, the friction number almost exponentially decreases as D decreases and, to a lesser extent, as L∕D increases. For D>400μm, the friction number approaches the theoretical Hagen–Poiseuille for macrotubes (64) when L∕D>∼1500, but higher values at smaller L∕D. The developed semiempirical analytical expression for calculating the friction number is in good agreement with the numerical and experimental results. The results suggest the presence of a velocity slip in the experiments and the plausible presence of a thin nanolayer at the walls of the microtubes. For D>200μm, this layer, if exists, is estimated to be ∼18.9nm, but increases to ∼21.5nm for D<200μm, when R¯e=800 and L∕D=1479.